We look at the division of 77564 by 45 
We want to divide 77564 by 45.

Advancing to step 1:
If we divide 7 by 45, we get 0 and a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 45

Going ahead to step 2:
When dividing 77 by 45, we get 1 with a remainder of 32.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 45 from 77 to get 32.
Bring next digit (5) of the dividend behind the 32 and repeat the process: 325 / 45

Let's proceed to step 3:
45 goes into 325 7 times with a remainder of 10.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
Subtract 315 from 325 to get 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 45

Step 4:
When dividing 106 by 45, we get 2 with a remainder of 16.
The next digit of our result is 2. 
Result so far: 172.0
Deduct 90 from 106 and we're left with 16.
Include the next digit (4) from the dividend after 16, then repeat: 164 / 45

Going ahead to step 5:
164 divided by 45 is 3 with a remainder of 29.
Put 3 as the next digit of the answer. 
Result so far: 1723.0
If we take 135 away from 164, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 6:
290 divided by 45 is 6 with a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 1723.6
The remainder is 20 after subtracting 270 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 7:
45 goes into 200 4 times with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 1723.64
Subtracting 180 from 200 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 1723.644
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 1723.644 with a remainder of 0.002.